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The Novikov conjecture for hyperbolic foliations. (La conjecture de Novikov pour les feuilletages hyperboliques.) (French) Zbl 0932.19005
In their paper “Groupes ‘boliques’ et conjecture de Novikov” [C. R. Acad. Sci., Paris, Sér. I 319, No. 8, 815-820 (1994; Zbl 0839.19003)], G. Kasparov and G. Skandalis have introduced a property of metric spaces and groups called bolicity. This property is more general than Gromov’s hyperbolicity. They were able to show that for such groups the Baum-Connes map \(\mu\) is injective and the Novikov conjecture holds.
The present paper is the publication of a thesis written under the direction of Skandalis. It is a generalization of the results of Kasparov and Skandalis to bolic foliations with compact base and whose holonomy groupoid is Hausdorff. The paper contains detailed proofs and at one stage a simplification of the original argument of Kasparov and Skandalis.

19K35 Kasparov theory (\(KK\)-theory)
46L87 Noncommutative differential geometry
46L80 \(K\)-theory and operator algebras (including cyclic theory)
20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
22A22 Topological groupoids (including differentiable and Lie groupoids)
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